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arXiv · 1503.00990

On the irreducible components of globally defined semianalytic sets

José F. Fernando
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Abstract

In this work we present the concept of amenable $C$-semianalytic subset of a real analytic manifold $M$ and study the main properties of this type of sets. Amenable $C$-semianalytic sets can be understood as globally defined semianalytic sets with a neat behavior with respect to Zariski closure. This fact allows us to develop a natural definition of irreducibility and the corresponding theory of irreducible components for amenable $C$-semianalytic sets. These concepts generalize the parallel ones for: complex algebraic and analytic sets, $C$-analytic sets, Nash sets and semialgebraic sets.

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José F. Fernando. 2015-03-03. On the irreducible components of globally defined semianalytic sets. https://arxiv.org/abs/1503.00990

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